定理的

Of mathematical theorems to study the self-questioning approach: This theorem is presented in the context of how come?

对数学定理学习的自我提问方式：这个定理是在怎样的背景下提出来的？

In chapter 1, similarity and perturbations of nest subalgebras of factor von Neumann algebras are studied. A similarity theorem is given (see Theorem 1. 2. 3), and it is shown that similar nests in a factor von Neumann algebra are close.

第一章研究因子von Neumann代数中套的相似性和套子代数的摄动，获到一个相似定理（定理1.2.3），其几何意义是：因子von Neumann代数中相似的套聚拢在一起并可向外扩展。

As the first step, the usage of the important theorem of the Sobolev space supplies some exciting conclusions by discussion of the method of protruding analysis and the function of energy with the positive and negative cases being considered.

采用能量函数方法和改进的凸性分析方法，从Sobolev空间的重要定理——嵌入定理入手，分初始能量为正或者为负两种情况，对所述问题进行讨论，得到了令人满意的结果。

1Because some conditions can not be fulfilled,one can not applythe known results in stochastic approximation directly.

1由于有些条件不能满足，现有的随机逼近结果无法直接利用，我们巧妙地克服了这一困难，在较弱的条件(文中H.4.1—H.4.3)下，给出了这类算法的严格收敛性分析(定理4.3.2，定理4.3.3)。

In the third chapter, we study complete minimal submanifolds of locallysymmetric space, and we obtain a pinching theorem about the Ricci curvature of the minimal submanifolds, which generalizes the result of Norio Ejiri\'s from sphere space to locally symmetric space.

第三章节研究局部对称空间中具有正Ricci曲率的完备极小子流形，得到了关于子流形Ricci曲率的一个pinching定理，该定理把Norio Ejiri的结论从外围空间为球空间推广到局部对称空间中。

In this thesis, we mainly study problems on global geometry and geometricanalysis of Riemannian submanifolds, including vanishing theorem for homologygroups, topological sphere theorem, L~2 harmonic 1-forms, finiteness of end andthe spectrum of the Laplacian. In 1973, by using the Federer-Fleming existence theorem and the techniquesfrom the calculus of variations in the geometric measure theory, H.

本文着重研究黎曼子流形上整体几何与几何分析的若干问题，主要内容包括子流形的同调群消没定理、拓扑球面定理、L~2调和1-形式、端的有限性和Laplace算子谱等问题。

In this paper a decision method of uniform convergence for function sequence is given, and a few of properties for the uniformly convergent function-sequence are obtained by this method, which is used in the construction of a new uniformly convergent function-sequence by others known.

给出了一个定理用于判定函数列的一致收敛，通过此判定定理，又得出了由一致收敛函数列构造新的一致收敛函数列的几个性质。

A comparison is made between the electrostatic field and universal gravitation field to find out the very similarities between them.

在比较静电场与万有引力场相似性的基础上，归纳出相似性的本质，进而根据相似性由静电场中已有的公式、定理及解题方法推导出万有引力场中与此相似的公式、定理及解题方法。

In this paper, the effects to image reconstruction by adopting different ways of sequence's truncation in unrelaxed iterative algorithm is discussed and further studying on the conditions to iterative reconstruction with phase -only have been done.

Sh~n在1949年发表了采样定理，提出在一定条件卜，可以用离散采样值重构带限连续信号。七十年代，l铭an等人提出了几个从零交叉点重构带通或带限信号的定理及其算法。1983年J.L.C.Salu和T.S.Huang对各种关于频谱有限信号外推问题的算法进行分析，提出了统一的迭代算法。

We can determine the unexistence of limit cycles of original 2D digital system by analysing the system set.

定理3和定理4所分析的2-D数字系统存在多个多重非线性的情况，则是Fahmy[41]和Agathoktis[30]所无法分析的。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。